bulb looking good and being good are two different things. I've encountered bulbs that appear to be solid, but have failed. I recommend swapping bulbs with a known good to prove the bulb is good/bad, first.

After that, you can connect a multimeter to the bulb plug to determine if the bulb is getting electricity. That'll give you a starting point for failure. You could even do the multimeter test first. Just put it to 12V and connect the tool to the bulb plug to complete the circuit. You should get anything from 11.5 to 14.2 volts, depending on the battery charge, and whether or not your engine is running with the alternator charging the system.

. If just the third light is working I would crawl under the truck and play with the connections where the rear harness connects to the harness from the front. It should be on a crossmember above where your spare tire is located. Those connections are known to corrode and cause issues.

Not weird at all. Happens more frequently than folks realize, though not frequently enough that any individual wouldn't likely encounter it more than once or twice in the life of a vehicle, if at all. The electrical connections get a patina of oxidation on them that prevents a solid electrical connection. The action of sliding the bulb in and out basically scraped off the patina and restores the connection. Re-seating the bulb basically "fixes" the problem. BTW, this is why dielectric grease is a good thing. It prevents oxidation of the components by prevent oxygen from reaching the metal.

Some folks may question how the oxidation can occur between two contact points, and the answer is that the contact points aren't fixed. Heat expansion actually results in slight movement between the connection points eventually allowing oxidation to creep between the connection points. The vibration of a vehicle often prevents the connection points from actually getting enough oxidation (the vibration keeps the oxidation from forming too thick) to prevent solid electrical connection, but as you encountered "often" is not "always".

Yes, it could have been corrosion, but, I suspect the two new bulbs fixed the problem. No, they didn't burn out together, one went first and then the 2nd followed shortly after. Bulbs have a defined life span, being used together, one will burn out and the other will quickly follow. You just didn't notice the first one being out, and then someone said "Hey, you don't have any brake lights".